課程名稱︰物理化學下 課程性質︰必修 課程教師︰陳逸聰 開課學院：生農學院(理學院開課) 開課系所：農化系(化學系開課) 考試日期（年月日）︰2009/04/14 考試時限（分鐘）：115分鐘 是否需發放獎勵金：是 （如未明確表示，則不予發放） 試題 : 1. The chemical reaction 2NO + H2 → N2O + H2O has the reaction mechanism of k1 (i) 2NO ←─→ N2O2 k-1 k2 (ii) N2O2 + H2 ─→ N2O + H2O (a)Use steady-state spproximation ti derive the rate of reaction. (6%) (b)When the reaction process (i) is slow and the reaction process (ii) is fast, reduce the rate of reaction in (a). (2%) (c)When the reaction process (i) is fast and the reaction process (ii) is slow, reduce the rate of reaction in (a). (2%) 2. A reaction is zero order in substance S. Starting with the differential rate law, derive an expression for t(1/2) in terms of the starting con- centration [S]0 and the zero-order rate consant k. (5%) 3. Consider the following proposed mechanism for the reaction A→P : k1 k4 A ←─────→ B ───→ P ↖ k-1 ↗ k-3╲k3 k2╱k-2 ↘ ↙ C (a)Write a differential equation for the rate of formation of B. (3%) (b)The formation of B from A and C is fast to equilibrium with equilibrium constants K1 = k1/k-1 , K2 = k2/k-2 , K3 = k3/k-3 , K4 is much smaller than all other Ks. Write a differential equation for the formation of P in terms of concentration of A, equilibrium cinstants, and k4. (3%) (c)Write an expression (containing no derivatives) for the concentration of P as a function of time. At zero time, [A]=[A]0 and [B],[C],[P]=0.(8%) 4. A and B react stoichiometrically to form P. If 0.01M A and 10M B are mixed, it is found that the log of the concentration of A vs. time is a straight line. (a)What is the order of the reaction with respect to A? (b)Write a one-line mechanism that is consistent with the kinetics and stoichiometry. (c)According to your mechanism, What is the order of the reaction with respect to B? (d)The half-life for the disappearance of A is 100s. What would be the predicted half-life if the concentration of B is changed from 10M to 20M? (e)From the half-life given in part (d), calculate the rate constant for the reaction of A with B. Specify the units of the rate constant. (15%) 5. Consider the simple Michaelis-Menten mechanism for an enzyme-catalyzed reaction: k1 k2 E + S ←──→ ES ──→ E + P K-1 The following deta were obtained: k1, k-1 very fast k2 = 100s^-1, K(M) = 1.0*10^-4M at 280K k2 = 200s^-1, K(M) = 1.5*10^-4M at 300K (a)For [S] = 0.10M and [E]0 = 1.0*10^-5M, calculate the rate of formation of product at 280K. (b)Calculate the activation energy for k2. (c)What is the value of the equilibrium constant at 280K for the formation of the enzyme-substrate complex ES from E and S? (d)What is the sign and magnitude of the standard thermodynamic enthalpy ΔH0 for the formation of ES from E and S? (12%) 6. Consider the following mechanism for the role of an inhibitor I of an enzyme: k1 k2 E + S ←──→ ES ───→ E + P k-1 k3 E + I ←──→ EI k-3 The concentration of [S] and [I] are much larger than the total enzyme concentration [E]0. Derive an expression for the rate of appearance of products. (8%) 7. For the enzyme succinoxdase, which adds oxygen to succinate to give fumarate, the following rate data were determined for a solution in which the enzyme concentration is 10.0μM. ┌─────────┬──┬──┬──┬──┬──┐ │[S] (mM) │0.33│0.50│1.00│2.00│10.0│ ├─────────┼──┼──┼──┼──┼──┤ │v (μM/s) at 20度C│0.50│0.62│0.79│0.99│1.17│ ├─────────┼──┼──┼──┼──┼──┤ │v (μM/s) at 40度C│2.41│2.99│3.81│4.78│5.65│ └─────────┴──┴──┴──┴──┴──┘ (a)What are the values of the Michaelis constants K(M) for this enzyme at the two temperatures? (b)What are the values of the rate constant k(cat) for this enzyme at the two temperatures? (c)What is the activation energy for the reaction? (d)Would you expect the activation energy to be higher or lower for the same reaction in the absence of enzyme? Explain. (12%) 8. Terminology and illustration. (24%) (a) Uncertainly principle. (b) The operator form of linear momentum. (c) Photoelectric effect. (d) Half-time (t(1/2)). (e) Transition state and activated complex. (f) Quantum yield (ψ). (g) Beer-Lambert law. (h) Sigmoid dependence. --

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